How to make bones visible through only one object
You can't make object A always be displayed in front of B, but perspectively occluded by C in the current Blender.

The common practice is to create rigs (bones or custom shaped bones) that don't occlude by choosing wireframe shapes. A quick way to achieve this, is to set the Maximum Draw Type (under Properties Panel > Object Tab > Display Section) to Wire. The Armature will always be display as wireframe, making the objects "behind" it easy to see.